Monday, January 30, 2017

A theoretical picture of the Mott insulating phase of organic charge transfer salts [such as (BEDT-TTF)2X] is that they can be described by a single-band Hubbard model on an anisotropic triangular lattice at half filling. The spin excitations can then be described by the corresponding Heisenberg model. In these models, each lattice site corresponds to a single anti-bonding orbital on a pair (dimer) of BEDT-TTF molecules. Thus the internal structure of the dimer and the corresponding two-band Hubbard model at three-quarters filling is "integrated out" leaving a one-band picture.

However, there are some dielectric relaxation experiments that can be interpreted as inconsistent with the picture above.
The key question is whether there is charge order within the dimer, in particular, does it have a net dipole moment?A 2010 theory paper by Hotta proposed this and an effective Hamiltonian for the Mott insulating phase where the spin on the dimer and the dipoles are coupled together. She suggested that a spin liquid phase could be driven by the dipoles, rather than spin frustration.
This picture also leads to the possibility of a multiferroic phase: coexisting ferromagnetic and ferroelectric phases.

There are two helpful recent reviews, presenting alternative views of the experiments.

The figure below shows experimental measurements from this paper. (The authors of the first review above and Hotta are co-authors.) The figure shows the temperature dependence of the real part of the dielectric constant at different frequencies. Note how it becomes very large at low frequencies (almost static) near about 25 K, which coincidentally is the temperature at which this organic charge transfer salt becomes antiferromagnetic (with weak ferromagnetism due to spin canting).

The above dielectric behaviour is similar to what one sees at a ferroelectric transition.

However, one should be cautious about this interpretation for multiple reasons. These are tricky experiments.

Dielectric dispersion spectroscopy is a bulk probe, not a microscopic one. One is not measuring the electric dipole moment of a single unit cell but rather the electric polarisation of a bulk crystal that has surfaces and contains defects, and impurities. For example, charge accumulation on the sample surface can enhance the measured dielectric constant and lead to significant frequency dependence, even when the actual material has no intrinsic frequency dependence (This is known as Maxwell-Wagner polarisation or the space-charge effect).

There are reports of significant sample dependence; the dielectric constant can vary by up to two orders of magnitude!

The origin of the dependence of the results on the direction of the electric field is not clear (at least to me). One usually finds the largest effects when the electric field is parallel to the least conducting direction (i.e. perpendicular the layers) in the crystal.

The magnitude of the electric dipole moment that one deduces from the magnitude of the dielectric constant (by fitting the temperature dependence to a Curie form, as in the dashed line in the figure above) is an order of magnitude larger than the moment on single dimers that is deduced from infrared (IR) measurements. This last discrepancy is emphasized by the authors of the second review above.

(IR measures the vibrational frequencies of the BEDT-TTF molecules; spectral shifts are correlated with the charge density on the molecule. Splitting of spectral lines corresponds to the presence of charge order, as discussed here.)

If one does accept that charge order occurs, further questions that arise include:

How do we know that the charge order is occurring within the dimers not between dimers?

Are these dielectric properties necessary or relevant for the insulating, superconducting, and magnetic properties (antiferromagnetism or spin liquid) or is it just a second-order effect (causality or correlation)?

What is the relevant effective Hamiltonian in the Mott insulating phase?

How is this similar and different to multiferroic behaviour in inorganic materials?

The key to understanding how H/D substitution changes the electronic state is that there is a hydrogen bond between two of the organic molecules with an oxygen-oxygen distance of 2.45 A. As highlighted (and explained) in this paper, around this distance the geometric isotope effect is largest (the H bond length increases to almost 2.5 A), leading to a significant change in the energy barrier for proton transfer.

The figure below nicely shows, using DFT-based calculations and the measured crystal structures for both isotopes at two different temperatures, how the barrier changes, leading to a change in the charge state of the molecules.
The H and D isotopes are at the top and the bottom, respectively.

Monday, January 23, 2017

A spin liquid is a state of matter where there is no magnetic order (spontaneous breaking of spin rotational symmetry) at zero temperature. The past few decades has seen a desperate search for both real materials and Heisenberg spin models in two spatial dimensions that have this property. I have written many posts on the subject. An important question is what is a definitive experimental signature of such a system.

One experimental signature is the temperature dependence of the specific heat. In particular, some theories predict spin liquid states with spinon excitations with a Fermi surface. This would lead to a linear term in the temperature dependence of the specific heat, as one sees in a simple metal that is a Landau Fermi liquid. This paper is one of several that claims to observe this signature.

However, it is important to bear in mind two subtle issues with interpreting these experiments.

First, one always have to subtract off the large contribution to the specific heat from lattice vibrations. There are two main ways to do this. One is to fit the data, including a cubic term, T^3 in the temperature dependence. The second method is to subtract the data from a different compound (e.g. a deuterated one) which has a different electronic (magnetic) ground state but a similar crystal structure. Due to subtle isotope effects and hydrogen bonding, sometimes deuterated compounds are argued to meet this requirement for the magnetic contributions to be different and the phonon contributions to be the same.

However, there are problems with both of these subtraction methods.

First, curve fitting with many parameters can be getting the tail of the elephant to wiggle, as discussed more below. Second, changing the chemistry does change the phonon spectrum and so also changes the lattice contribution.

Finally, what about the linear in T term?

In a News and Views about a 2008 Nature Physics paper claiming to observe this linear in T term, Art Ramirez showed one could take the same experimental data and fit it to an alternative expression involving T^(2/3) which was proposed by an alternative theory.

This is shown in the Figure below.

I also worry about how the low T specific heat is dominated by the 1/T^2 term associated with the Schottky anomaly from two level systems.

Unfortunately, Ramirez's concerns seem to have been ignored in following papers.

We really need more direct experimental probes of spin liquid behaviour. Unfortunately, there is a paucity of realistic ones.

Thursday, January 19, 2017

I am on the lookout for good videos that meet roughly the following criteria:
-available free online
-on condensed matter or chemistry
-accessible and interesting to a popular audience
-represent the science in a reasonable and helpful way
-lack hype

This is motivated by the following experience. I knew that there were people (mostly young) who will spend endless hours watching trashy videos (whether B-grade movies or silly antics) on Youtube. However, I only recently learned that there are also people who will spend hours watching videos on serious subjects (science, politics, history, religion, ...)

I am keen to find such material so I can recommend it as alternatives to the kind of thing featuring Michio Kaku or string theory propaganda from Brian Greene.

Tuesday, January 17, 2017

Too often I encounter papers or people that describe some detailed study of a particular region of the parameter space of some effective model Hamiltonian (Hubbard, Holstein, Hofstadter, ...) and I am left wondering, "why are you doing this?"

The most cynical answers I sometimes fear are "well, it is there" [just like Mount Everest], "no one has done this before", and "I can get a paper out of this."

It is not hard to find regions of unexplored parameter space for most models. One can simply add next-nearest neighbour hopping terms, change the lattice (anisotropic, triangular, Kagome, honeycomb, ...) , or add more Coulomb or exchange interactions, or add a magnetic flux, ....
The list is almost endless.
But, so what?

Here are a few good reasons of why exploring a particular parameter regime may be worth doing. Only one of them is sufficient. Often only one may be true.

In this parameter regime:

A1. There is an actual material that is believed to be described by this Hamiltonian.

A2. Given the inevitable uncertainty in the actual parameters for a specific material it is worth knowing how much calculated properties change as the parameters are varied.

B. There may be a new phase of matter or at least qualitatively different behaviour.

C. One can gain physical insight into the model.

D. A particular analytical approximation or numerical method is known to be reliable.

E. Provides a good testing ground for the reliability of a new analytical approximation or numerical method.

Friday, January 13, 2017

Today is the last day of my vacation and so on monday I will be back to serious (?!) blogging about science. In the mean time...

On a recent long flight I enjoyed watching many episodes of Silicon Valley, a TV sitcom (?) that is a satire of start up companies. I thought it was pretty funny. [But maybe that was the long flight...]
This clip is a good sample.

The show reminded me of Utopia, an Australian TV satire of government bureaucracy.
Both shows do well at pillorying the personalities who peddle management, marketing, money, and metrics (M^4! ) and have a disproportionate influence on the direction of things. Universities are fertile for similar satire.

A starting point for ideas could be The Department, a play written in 1975 by David Williamson, one of Australia's best-known playwrights. He had been a lecturer in mechanical engineering and social psychology for a number of years before writing the play.

Tuesday, January 10, 2017

I watched the first episode of The Forces of Nature narrated by Brian Cox, The Universe in a Snowflake.
[Unfortunately, I don't think the whole episode is free online. It should be! I watched it streamed through my university library website].

The imagery and creativity are stunning.
The episode focuses on shapes that occur in nature: spherical planets, human towers in Spain, hexagonal snowflakes, honeycomb beeswax, and "spherical" manatees, animals with bilateral symmetry, ...
Cox nicely discusses some of the underlying principles, including how complexity emerges from simple underlying laws.

During his Ph.D Henderson worked on a theory of quantum gravity at the University of Rochester in the 1990s. He then left physics for Wall Street and is now a science writer.

Here are a few comments.

First, as often happens in discussions that come up related to Woit's blog, I take umbrage at the common assumption that "theoretical physics" is equated with theories of elementary particles and string theory. The simplest argument against the narcissism of the proponents of this narrow view is that there are five Physical Review journals (A and E). Each contains (very roughly half) theory papers and only D is concerned with such topics.

Issues of emotional and mental health feature prominently; although, not as explicitly discussed as they could be.

The lack of direction and floundering in his research project on quantum gravity is unrepresentative of most Ph.D research in theoretical physics. It just suggests the field itself it at an impasse and is arguably unsuitable for Ph.D research.

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About Me

I have fun at work trying to use quantum many-body theory to understand electronic properties of complex materials.
I am married to the lovely Robin and have two adult children and a dog, Priya (in the photo). I also write an even more personal blog Soli Deo Gloria [thoughts on theology, science, and culture]

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Although I am employed by the University of Queensland and funded by the Australian Research Council all views expressed on this blog are solely my own. They do not reflect the views of any present or past employers, funding agencies, colleagues, organisations, family members, churches, insurance companies, or lawyers I currently have or in the past have had some affiliation with.

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